Question

x= 3 + 2√2

y= 4- √2

Oblicz:

a) x-y

b) x·y

c)x/y

Answer 1

a)

x - y = 3 + 2√2  -(4 - √2) = 3 + 2√2 - 4 + √2 = 3√2 - 1

b)

x * y = (3 + 2√2) *(4 - √2) = 12 - 3√2 + 8√2 - 2√2* √2 =

       = 12 + 5√2 - 4 = 8 + 5√2

c)

x/y =  (3 + 2√2)/(4 - √2) =  [ (3 + 2√2) (4 + √2) ] : [ (4 - √2) *(4 - √2) ]=

= ( 12 + 3√2 + 8√2 + 2√2*√2) : ( 16 - 2) = ( 12 + 11√2 + 4) : 14 =

= (16 + 11√2)/14